Concentration of Mass at Membrane Surface Calculator

✖Water flux is defined as the rate at which water flows through a membrane per unit area.ⓘ Water Flux [J_w]			+10% -10%
✖Mass transfer coefficient at membrane surface is defined as the measure of the rate at which solutes can diffuse through the membrane.ⓘ Mass Transfer Coefficient at Membrane Surface [k_l]			+10% -10%
✖Solute rejection is defined as the ability of a membrane to prevent the passage of solutes from a feed solution to the permeate solution.ⓘ Solute Rejection [R_']			+10% -10%
✖Bulk concentration is defined as the concentration of solutes in the bulk fluid, which is the fluid that is not in contact with the membrane.ⓘ Bulk Concentration [C_b]			+10% -10%

✖Solute concentration at membrane surface is defined as the concentration of solutes in the fluid immediately adjacent to the membrane surface.ⓘ Concentration of Mass at Membrane Surface [C_m]

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Formula

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Concentration of Mass at Membrane Surface

Formula

`"C"_{"m"} = exp("J"_{"w"}/"k"_{"l"})/(("R"_{"'"}+(1-"R"_{"'"})*exp("J"_{"w"}/"k"_{"l"})))*"C"_{"b"}`

Example

`"4.206205"=exp("0.0001139m³/(m²*s)"/"0.00003cm/s")/(("0.95"+(1-"0.95")*exp("0.0001139m³/(m²*s)"/"0.00003cm/s")))*"0.3"`

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Concentration of Mass at Membrane Surface Solution

STEP 0: Pre-Calculation Summary

Formula Used

Solute Concentration at Membrane Surface = exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)/((Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)))*Bulk Concentration
C_m = exp(J_w/k_l)/((R_'+(1-R_')*exp(J_w/k_l)))*C_b
This formula uses 1 Functions, 5 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Solute Concentration at Membrane Surface - Solute concentration at membrane surface is defined as the concentration of solutes in the fluid immediately adjacent to the membrane surface.
Water Flux - (Measured in Cubic Meter per Square Meter per Second) - Water flux is defined as the rate at which water flows through a membrane per unit area.
Mass Transfer Coefficient at Membrane Surface - (Measured in Centimeter per Second) - Mass transfer coefficient at membrane surface is defined as the measure of the rate at which solutes can diffuse through the membrane.
Solute Rejection - Solute rejection is defined as the ability of a membrane to prevent the passage of solutes from a feed solution to the permeate solution.
Bulk Concentration - Bulk concentration is defined as the concentration of solutes in the bulk fluid, which is the fluid that is not in contact with the membrane.

STEP 1: Convert Input(s) to Base Unit

Water Flux: 0.0001139 Cubic Meter per Square Meter per Second --> 0.0001139 Cubic Meter per Square Meter per Second No Conversion Required
Mass Transfer Coefficient at Membrane Surface: 3E-05 Centimeter per Second --> 3E-05 Centimeter per Second No Conversion Required
Solute Rejection: 0.95 --> No Conversion Required
Bulk Concentration: 0.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_m = exp(J_w/k_l)/((R_'+(1-R_')*exp(J_w/k_l)))*C_b --> exp(0.0001139/3E-05)/((0.95+(1-0.95)*exp(0.0001139/3E-05)))*0.3

Evaluating ... ...

C_m = 4.20620545123437

STEP 3: Convert Result to Output's Unit

4.20620545123437 --> No Conversion Required

FINAL ANSWER

4.20620545123437 ≈ 4.206205 <-- Solute Concentration at Membrane Surface

(Calculation completed in 00.004 seconds)

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Shri Guru Gobind Singhji Institute of Engineering and Technology (SGGS), Nanded

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< 16 Basics of Membrane Separation Processes Calculators

Concentration of Mass at Membrane Surface

Go Solute Concentration at Membrane Surface = exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)/((Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)))*Bulk Concentration

Partial Molar Volume of Water based on Solution Diffusion Model

Go Partial Molar Volume = (Mass Water Flux*[R]*Temperature*Membrane Layer Thickness)/(Membrane Water Diffusivity*Membrane Water Concentration*(Membrane Pressure Drop-Osmotic Pressure))

Water Permeability based on Initial flux

Go Water Permeability Through Membrane = Volumetric Water Flux Through Membrane/(Applied Pressure Driving Force*(1-(([R]*Temperature*Molecular Weight)/(Initial Volume*Applied Pressure Driving Force))))

Time of Dialysis using Hollow Fiber Haemodialyser

Go Time of Dialysis = (Volume of blood/Volumetric Rate of Blood)*ln(Initial Concentration In Blood/Final Concentration In Blood)*((1-(e^-No of Transfer Units))^-1)

Hagen Poiseuille Based Flux for Membrane Separation

Go Flux through Membrane = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Tortuosity*Membrane Thickness)

Liquid Viscosity Based On Hagen Poiseuille Equation

Go Liquid Viscosity = (Pore Diameter^2*Membrane Porosity*Applied Pressure Driving Force)/(32*Flux through Membrane*Tortuosity*Membrane Thickness)

Tortuosity Factor of Pores

Go Tortuosity = (Membrane Porosity*Pore Diameter^2*Applied Pressure Driving Force)/(32*Liquid Viscosity*Flux through Membrane*Membrane Thickness)

Pressure Difference across Pore based on Poiseuille's Law

Go Pressure Difference Across Pore = (Liquid Flow through Pore*128*Viscosity of Liquid*Length of Pore)/(pi*(Membrane Pore Diameter)^(4))

Liquid Flow through Pore Based On Poiseuilles Law

Go Liquid Flow through Pore = ((pi*(Membrane Pore Diameter)^4)/(128*Viscosity of Liquid*Length of Pore))*Pressure Difference Across Pore

Liquid Viscosity based on Poiseuille's Law

Go Viscosity of Liquid = (Pressure Difference Across Pore*pi*(Membrane Pore Diameter)^(4))/(Liquid Flow through Pore*128*Length of Pore)

Liquid Viscosity based on Membrane Resistance

Go Liquid Viscosity = Applied Pressure Driving Force/(Membrane Flow Resistance of Unit Area*Flux through Membrane)

Membrane Flux Based on Resistance

Go Flux through Membrane = Applied Pressure Driving Force/(Membrane Flow Resistance of Unit Area*Liquid Viscosity)

Resistance to flow in Membranes

Go Membrane Flow Resistance of Unit Area = Applied Pressure Driving Force/(Liquid Viscosity*Flux through Membrane)

Applied Pressure Driving Force Based on Permeability of Membrane

Go Applied Pressure Driving Force = Flux through Membrane/Water Permeability Through Membrane

Water Permeability through Membrane

Go Water Permeability Through Membrane = Flux through Membrane/Applied Pressure Driving Force

Membrane Flux Based on Water Permeability

Go Flux through Membrane = Water Permeability Through Membrane*Applied Pressure

Concentration of Mass at Membrane Surface Formula

On What Factors Does Concentration Of Mass At Membrane Surface Depends?

Solute concentration: The higher the solute concentration in the bulk fluid, the higher the solute concentration at the membrane surface.
Rate of solute transport: The faster the solutes are transported through the membrane, the lower the solute concentration at the membrane surface.
Fouling: The presence of fouling on the membrane surface can increase the solute concentration at the membrane surface.
Operating conditions: The operating conditions, such as the pressure and temperature, can affect the rate of solute transport through the membrane.
Membrane properties: The membrane properties, such as the pore size and the hydrophilicity/hydrophobicity, can affect the rate of solute transport through the membrane.

How to Calculate Concentration of Mass at Membrane Surface?

Concentration of Mass at Membrane Surface calculator uses Solute Concentration at Membrane Surface = exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)/((Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)))*Bulk Concentration to calculate the Solute Concentration at Membrane Surface, Concentration of mass at membrane surface is defined as the concentration of solutes in the fluid immediately adjacent to the membrane surface in a membrane separation process. Solute Concentration at Membrane Surface is denoted by C_m symbol.

How to calculate Concentration of Mass at Membrane Surface using this online calculator? To use this online calculator for Concentration of Mass at Membrane Surface, enter Water Flux (J_w), Mass Transfer Coefficient at Membrane Surface (k_l), Solute Rejection (R_') & Bulk Concentration (C_b) and hit the calculate button. Here is how the Concentration of Mass at Membrane Surface calculation can be explained with given input values -> 6 = exp(0.0001139/3E-07)/((0.95+(1-0.95)*exp(0.0001139/3E-07)))*0.3.

FAQ

What is Concentration of Mass at Membrane Surface?

Concentration of mass at membrane surface is defined as the concentration of solutes in the fluid immediately adjacent to the membrane surface in a membrane separation process and is represented as C_m = exp(J_w/k_l)/((R_'+(1-R_')*exp(J_w/k_l)))*C_b or Solute Concentration at Membrane Surface = exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)/((Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)))*Bulk Concentration. Water flux is defined as the rate at which water flows through a membrane per unit area, Mass transfer coefficient at membrane surface is defined as the measure of the rate at which solutes can diffuse through the membrane, Solute rejection is defined as the ability of a membrane to prevent the passage of solutes from a feed solution to the permeate solution & Bulk concentration is defined as the concentration of solutes in the bulk fluid, which is the fluid that is not in contact with the membrane.

How to calculate Concentration of Mass at Membrane Surface?

Concentration of mass at membrane surface is defined as the concentration of solutes in the fluid immediately adjacent to the membrane surface in a membrane separation process is calculated using Solute Concentration at Membrane Surface = exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)/((Solute Rejection+(1-Solute Rejection)*exp(Water Flux/Mass Transfer Coefficient at Membrane Surface)))*Bulk Concentration. To calculate Concentration of Mass at Membrane Surface, you need Water Flux (J_w), Mass Transfer Coefficient at Membrane Surface (k_l), Solute Rejection (R_') & Bulk Concentration (C_b). With our tool, you need to enter the respective value for Water Flux, Mass Transfer Coefficient at Membrane Surface, Solute Rejection & Bulk Concentration and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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